which of the statements a through i about the function ( y = f(x) ) graphed here are true, and which are…

which of the statements a through i about the function ( y = f(x) ) graphed here are true, and which are false?\na. the statement ( lim_{x \to 2} f(x) ) does not exist is false.\nb. the statement ( lim_{x \to 2} f(x)=2 ) is false.\nc. the statement ( lim_{x \to 1} f(x) ) does not exist is true.\nd. the statement ( lim_{x \to c} f(x) ) exists at every point ( c ) in ( (-1,1) ) is true.\ne. the statement ( lim_{x \to c} f(x) ) exists at every point ( c ) in ( (1,3) ) is true.\nf. the statement ( f(1)=-3 ) is false.\ng. the statement ( f(1)=0 ) is true.\nh. the statement ( f(2)=3 ) is true.\ni. the statement ( f(2)=1 ) is

which of the statements a through i about the function ( y = f(x) ) graphed here are true, and which are false?\na. the statement ( lim_{x \to 2} f(x) ) does not exist is false.\nb. the statement ( lim_{x \to 2} f(x)=2 ) is false.\nc. the statement ( lim_{x \to 1} f(x) ) does not exist is true.\nd. the statement ( lim_{x \to c} f(x) ) exists at every point ( c ) in ( (-1,1) ) is true.\ne. the statement ( lim_{x \to c} f(x) ) exists at every point ( c ) in ( (1,3) ) is true.\nf. the statement ( f(1)=-3 ) is false.\ng. the statement ( f(1)=0 ) is true.\nh. the statement ( f(2)=3 ) is true.\ni. the statement ( f(2)=1 ) is

Answer

Explanation:

Step1: Analyze limit at (x = 2)

For (\lim_{x\rightarrow2}f(x)), the left - hand limit and the right - hand limit are equal. So, (\lim_{x\rightarrow2}f(x)) exists.

Step2: Analyze (\lim_{x\rightarrow2}f(x)) value

From the graph, (\lim_{x\rightarrow2}f(x)=1\neq2)

Step3: Analyze limit at (x = 1)

At (x = 1), the left - hand limit (approaching from the left side of (x = 1)) and the right - hand limit (approaching from the right side of (x = 1)) are not equal. So, (\lim_{x\rightarrow1}f(x)) does not exist.

Step4: Analyze limit in ((-1,1))

In the open interval ((-1,1)), the function is continuous (no breaks or jumps). So, (\lim_{x\rightarrow c}f(x)) exists for every (c\in(-1,1))

Step5: Analyze limit in ((1,3))

In the open interval ((1,3)), the function is continuous (no breaks or jumps). So, (\lim_{x\rightarrow c}f(x)) exists for every (c\in(1,3))

Step6: Analyze (f(1))

From the graph, (f(1)=0\neq - 3)

Step7: Analyze (f(1))

From the graph, (f(1) = 0)

Step8: Analyze (f(2))

From the graph, (f(2)=1\neq3)

Step9: Analyze (f(2))

From the graph, (f(2)=1)

Answer:

a. False b. False c. True d. True e. True f. False g. True h. False i. True